We work with a local manufacturer to produce fair-trade certified tote bags and we want to review our labor strategy. Assume our production of tote bags follows the Cobb Douglas production function: Q = K^1/2L^1/2, and please note that our capital is fixed at 16 units (K=16). Please note that we have already covered our fixed cost of capital.

If we sell our fair-trade tote bags for $50 (P), and we pay an hourly wage rate to our workers equal to $10 (w), what is the optimal amount of labor to employ to maximize profits under the VMPL=w optimization rule?

Please make sure to report on what the optimal labor (L) is, resulting quantity (Q) produced, and resulting profit level.